Spectral analysis for the Gauss problem on continued fractions (Q2252946)

Using Proposition 2.1.5 from the monograph by the author and \textit{C. Kraaikamp} [Metrical theory of continued fractions. Dordrecht: Kluwer Academic Publishers (2002; Zbl 1122.11047)], we present a new derivation of the formula appearing in [\textit{K. I. Babenko}, Sov. Math., Dokl. 19, 136--140 (1978); translation from Dokl. Akad. Nauk SSSR 238, 1021--1024 (1978; Zbl 0389.10036)] and [\textit{D. Mayer} and \textit{G. Roepstorff}, J. Stat. Phys. 47, No. 1--2, 149--171 (1987; Zbl 0658.10057)] that gives the probability distribution of \(\tau^{-n}\) in terms of the eigenvalues of a symmetric operator. Here \(\tau\) is the well-known Gauss-map.